Infinite games and chain conditions

We apply the theory of infinite two-person games to two well-known problems in topology: Suslin’s Problem and Arhangel’skii’s problem on $G_{\delta }$ covers of compact spaces. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable and 2) in every compact space satisfying the game-theoretic version of the weak Lindel"of property, every cover by $G_{\delta }$ sets has a continuum-sized subcollection whose union is $G_{\delta }$-dense.